We study the homotopy fixed points under the Frobenius endomorphism on the stable A1-homotopy category of schemes in characteristic p>0 and prove a rigidity result for cellular objects in these categories after inverting p. As a consequence we determine the analogous fixed points on the K-theory of algebraically closed fields in positive characteristic. We also prove a rigidity result for the homotopy fixed points of the partial Frobenius pullback on motivic cohomology groups in weights at most 1.
Classification :
14F42, 14G17
Mots-clés :
rigidity, K-theory, homotopy theory
Affiliations des auteurs :
Timo Richarz
1
;
Jakob Scholbach
2
1
TU Darmstadt, Darmstadt, Germany
2
Università degli Studi di Padova, Padova, Italy
Timo Richarz; Jakob Scholbach. Frobenius rigidity in $\mathbb{A}^{1}$-homotopy theory. Documenta mathematica, Tome 30 (2025) no. 1, pp. 219-244. doi: 10.4171/dm/988
@article{10_4171_dm_988,
author = {Timo Richarz and Jakob Scholbach},
title = {Frobenius rigidity in $\mathbb{A}^{1}$-homotopy theory},
journal = {Documenta mathematica},
pages = {219--244},
year = {2025},
volume = {30},
number = {1},
doi = {10.4171/dm/988},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/988/}
}
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